Right
卑 supplies the sound — bēi unchanged.
卑 also lends a faint semantic flavour: it originally pictured a hand holding a ladle, marker of a low servant's role. A stele stands low and humble before history, recording deeds rather than boasting. Same phonetic in
啤 (beer),
脾 (spleen),
婢 (slave girl),
牌 (sign/plaque) — the last especially close to
碑 in meaning.